The amplitude and phase of an optical wave usually fluctuate. Coherence of light is used to describe the correlation of the fluctuations between two or more optical waves. Two optical waves are mutually coherent when the fluctuations in the optical waves are completely correlated. Conversely, when the fluctuations in two optical waves are totally uncorrelated, the optical waves are incoherent with respect to each other. In many practical optical systems, two light beams may be partially correlated in amplitude and phase to have a partial coherence.
The degree of coherence of two or more optical waves can significantly affect the total optical field produced by spatially overlapping the optical waves. When mutually incoherent optical waves intercept each other in space, the total optical intensity distribution in the region of superposition is simply a linear summation of the individual intensity distributions. However, if the optical waves are at least partially coherent with respect to one another, interference of the optical waves occurs and produces a non-linear superposition of the individual intensity patterns. This interference causes the intensity distribution of the total optical field to vary spatially between maxima which are larger than the sum of the individual peak intensities, and minima which may be zero due to the complete cancellation of the waves.
Optical interferometry uses the interference of two or more at least partially mutually coherent beams to extract information embedded in at least one of the beams. Various optical interferometers have been developed for measurements and optical probing. The Michaelson interferometer is a classical example of this type. A single monochomatic light source may be used to produce two mutually coherent beams which interfere to produce an interference pattern.
One application of the optical interferometry is characterization of a surface, i.e., surface topography. For example, the flatness or the curvature of a surface can be determined by using optical interferometric techniques. Optical interferometric techniques may be advantageously used to achieve real-time, remote, non-intrusive, full-field measurements of certain surfaces. In particular, an optical interferometric technique for measuring curvature and curvature change can be applied to measurements related to various surfaces in semiconductors, electronic components and other devices.
Determination of effects caused by thermal stress in thin films is one example of such applications. As the electronics industry demand increasingly smaller dimensions of metal interconnections and more complex multilayered structures, mechanical properties and stresses of thin films used for these interconnections become crucial to the lifetimes of ultra large scale integrated circuits. The difficulty in measuring the mechanical properties and stresses of interconnections increases as their sizes decrease. For example, one concern for the interconnection materials is residual stresses as a result of the fabrication process and additional stresses caused by thermal cycling.
Typically, integrated circuit metallization produce multiple layers on a semiconductor substrate (e.g., silicon), often at elevated temperatures. The layers usually exhibit different mechanical, physical and thermal properties which lead to high stresses in interconnection structures. These stresses can cause undesired stress-induced voiding and are directly related to electromigration. In addition, the stresses may cause cracking of the substrate.
Voiding, electromigration, and substrate cracking are among the leading failure mechanisms in integrated circuits. Information regarding stresses, stress distribution, and stress origins is an important step in improving reliability of integrated circuits.
One approach to determine stresses in films uses x-ray diffraction to directly measure strains in polycrystalline materials by measuring d-spacings of a single reflection for several orientations of the sample. This is disclosed in Elements of X-ray diffraction, by Cullity, Addison-Wesley, Reading, Mass. (1978).
Another approach measures substrate curvature or deflection to determine stresses based on a correlation between the curvature change and the stress. The curvature or curvature change may be measured by, for example, scanning a laser beam from point to point on a surface or using a Twyman-Green interferometer with two successive differentiations of the experimental data.
Diffraction of x-rays from single crystal substrates is also commonly used to measure curvatures of certain surfaces. In essence, the change in directions of incident and diffracted beams by a surface caused by a translation of the surface is used to determine the surface curvature. See, for example, Vreeland et al. in Materials Research Society Proceedings, Vol. 30 (3), 1988. The curvature is determined in an averaged sense over the point of initial beam incidence and the point of beam incidence after translation. Since a rigid body rotation may occur during the required specimen translation, a calibration process is usually required to correct the error caused by such rotation. This can be done by using a substantially flat reference specimen of the same crystallographic structure which may be part of the same single crystal wafer under measurement. Hence, the measured curvatures of this technique are relative to the reference specimen.